1. Field
Apparatuses and methods consistent with exemplary embodiments relate to encoding and decoding an image, and more particularly, to transforming and inverse-transforming a block having a large size.
2. Description of the Related Art
According to a current international video coding standard, such as H.264 or MPEG-4, a video signal is hierarchically divided into a sequence, a frame, a slice, a macroblock, and a block, wherein the block is a minimum processing unit. In terms of encoding, a prediction remaining error of the block is determined via intra-frame or inter-frame prediction, block transformation is performed such that energy is focused on a coefficient of a decimal, and image data is compressed and recorded as a coded bitstream via quantization, scanning, run length coding, and entropy coding. In terms of decoding, processes are performed in the opposite order. First, a block transformation coefficient of entropy coding is extracted from a bitstream. Then, a prediction remaining error of a block is reconstructed via inverse-quantization and inverse-transformation, and prediction information is used to reconstruct video data of the block. In an encoding-decoding process, a transformation module is a base of video compression, and transformation performance of the transformation module directly affects general performance of a codec.
Discrete cosine transform (DCT) is employed in an initial video coding standard, such as MPEG-1 or H.261. After the DCT was introduced in 1974, the DCT has been widely used in image and video coding fields. Transformation performance of the DCT is excellent compared to all sub-optimal transforms since the DCT removes correlation of image elements in a transformation domain and prepares a base for high efficiency image compression. However, since a DCT matrix is expressed using a floating point number, many system resources are used due to massive floating point operations. Accordingly, a new DCT algorithm is required so as to improve transformation efficiency while performing transformation on a block having a large size.